FUNCTION: Bump - insert a word into a tableau

CALLING SEQUENCE:

Bump(t, w)

TAB[Bump](t, w)

PARAMETERS:

t = any list of list(s) denoting a tableau

w = any word

SYNOPSIS:

• The Bump function inserts a word [x1, x2, ...] into a tableau from the right. It first inserts x1, then x2, and so on.

• The insertion algorithm is due to Schensted.

• When called with the 'nil' option as third argument, the Bump function nilplactically inserts the word into the tableau from the right.

• The nilplactic insertion algorithm makes Bump([], w[1,2,1], 'nil') equal to Bump([], w[2,1,2], 'nil') (Coxeter relations). Whenever the result of the insertion is not a reduced decomposition, it returns [].

• Whenever there is a conflict between the function name Bump and another name used in the same session, use the long form TAB['Bump'].

EXAMPLES:

> with(TAB):
> t:=[[3], [2,6,8]]:
> Tab2Mat(Bump(t, w[4,1]));
 
                                 [ 3       ]
                                 [         ]
                                 [ 2  6    ]
                                 [         ]
                                 [ 1  4  8 ]
 
> t:=[[2,3], [1,2]]:
> Tab2Mat(Bump(t, w[3,1], 'nil'));
 
                                 [ 3       ]
                                 [         ]
                                 [ 2  3    ]
                                 [         ]
                                 [ 1  2  3 ]